To answer the topic, I'm gonna say no. It feels like an extra kick to the junk to think that the whole series is just something like TATV.
But I could buy Enterprise being a universe that was affected by Picard and crew during first contact...Which could lead to the Kelvin-Trek films seeing how Enterprise could have a Earth-Romulan war that...Was a lot less secretive to the point nobody in Kelvin-Kirk's time was too surprised what Romulans actually look like as long as nobody starts shooting.
But I could buy Enterprise being a universe that was affected by Picard and crew during first contact...Which could lead to the Kelvin-Trek films seeing how Enterprise could have a Earth-Romulan war that...Was a lot less secretive to the point nobody in Kelvin-Kirk's time was too surprised what Romulans actually look like as long as nobody starts shooting.